Simplifications Involving Infinity [FEATURE]

[andrew-murdza]

Implement these simplification rules

Base of Infinity

• {match:'\infty^a',replace:'\infty',condition:'a>0'}
• {match:'\infty^a',replace:'0',condition:'a<0'}
• {match:'(-\infty)^a',replace:'0',condition:'a<0'}
• {match:'(-\infty)^n',replace:'\infty',condition:'a is a even integer'}
• {match:'(-\infty)^{n/m}',replace:'\infty',condition:'n is an even integer and m is an odd integer'}
• {match:'(-\infty)^n',replace:'-\infty',condition:'a is an odd integer'}
• {match:'(-\infty)^{n/m}',replace:'\infty',condition:'n is an odd integer and m is an odd integer'}
• Roots use the same rules as powers (probably don't need code for this)

Power of Infinity

• {match:a^\infty,replace:'\infty',condition:'a>1'}
• {match:a^\infty,replace:'0',condition:'0<a<1'}
• {match:a^{-\infty},replace:'0',condition:'a>1'}
• {match:a^{-\infty},replace:'\infty',condition:'0<a<1'}
• \exp(\infty)->\infty
• \exp(-\infty)->0

Log of Infinity

• \log(\infty)->\infty
• \ln(\infty)->\infty

Trig functions

• \sin(\infty)->NaN
• \cos(\infty)->NaN
• \tan(\infty)->NaN
• \cot(\infty)->NaN
• \sec(\infty)->NaN
• \csc(\infty)->NaN
• \sin(-\infty)->NaN
• \cos(-\infty)->NaN
• \tan(-\infty)->NaN
• \cot(-\infty)->NaN
• \sec(-\infty)->NaN
• \csc(-\infty)->NaN

Inverse Trig Functions

• \arcsin(\infty)->NaN
• \arccos(\infty)->NaN
• \arcsin(-\infty)->NaN
• \arccos(-\infty)->NaN
• \arctan(\infty)->\frac{\pi}{2}
• \arctan(-\infty)->-\frac{\pi}{2}
• \arccot(\infty)->0
• \arccot(-\infty)->\pi
• \arcsec(\infty)->\frac{\pi}{2}
• \arcsec(-\infty)->\frac{\pi}{2}
• \arccsc(\infty)->0
• \arccsc(-\infty)->0

Hyperbolic Trig Functions

• \sinh(\infty)->\infty
• \sinh(-\infty)->-\infty
• \cosh(\infty)->\infty
• \cosh(-\infty)->\infty
• \tanh(\infty)->1
• \tanh(-\infty)->-1
• \coth(\infty)->1
• \coth(-\infty)->-1
• \sech(\infty)->0
• \sech(-\infty)->0
• \csch(\infty)->0
• \csch(-\infty)->0

Inverse of Hyperbolic Trig Functions

• \arcsinh(\infty)->\infty
• \arcsinh(-\infty)->-\infty
• \arccosh(\infty)->\infty
• \arccosh(-\infty)->NaN
• \arctanh(\infty)->NaN
• \arctanh(-\infty)->NaN
• \arccoth(\infty)->NaN
• \arccoth(-\infty)->NaN
• \arcsech(\infty)->NaN
• \arcsech(-\infty)->NaN
• \arccsch(\infty)->0
• \arccsch(-\infty)->0